In a two-way ANOVA, where a is the number of factor A levels and b is the number of factor B levels, which of the following expressions gives the number of the degrees of freedom for the "error term"?
A) (a - 1)(b - 1)
B) n - ab
C) (a - 1) + (b - 1)
D) abn + 1

Question

Quizplus · Accepted Answer

The error term in a two-way ANOVA represents the variability within each treatment combination. The degrees of freedom for the error term is calculated as the total number of observations minus the degrees of freedom for the main effects and the interaction effect. In this case, the total number of observations is ab, the degrees of freedom for the main effects are (a - 1) and (b - 1), and the degrees of freedom for the interaction effect is (a - 1)(b - 1). Therefore, the degrees of freedom for the error term is ab - (a - 1) - (b - 1) - (a - 1)(b - 1) = n - ab.

In a Two-Way ANOVA, Where a Is the Number of Factor